Varying disc-magnetosphere coupling as the origin of pulse profile variability in SAX J1808.4-3658

Accreting millisecond pulsars show significant variability of their pulse profiles, especially at low accretion rates. On the other hand, their X-ray spectra are remarkably similar with not much variability over the course of the outbursts. For the first time, we have discovered that during the 2008 outburst of SAX J1808.4-3658 a major pulse profile change was accompanied by a dramatic variation of the disc luminosity at almost constant total luminosity. We argue that this phenomenon is related to a change in the coupling between the neutron star magnetic field and the accretion disc. The varying size of the pulsar magnetosphere can influence the accretion curtain geometry and affect the shape and the size of the hotspots. Using this physical picture, we develop a self-consistent model that successfully describes simultaneously the pulse profile variation as well as the spectral transition. Our findings are particularly important for testing the theories of accretion onto magnetized neutron stars, better understanding of the accretion geometry as well as the physics of disc-magnetosphere coupling. The identification that varying hotspot size can lead to pulse profile changes has profound implications for determination of the neutron star masses and radii.Comment: 12 pages, 5 figures and 3 tables; accepted to MNRA

Supersymmetry for Fermion Masses

It is proposed that supersymmetry (SUSY) maybe used to understand fermion mass hierarchies. A family symmetry Z_{3L} is introduced, which is the cyclic symmetry among the three generation SU(2) doublets. SUSY breaks at a high energy scale ~ 10^{11} GeV. The electroweak energy scale ~ 100 GeV is unnaturally small. No additional global symmetry, like the R-parity, is imposed. The Yukawa couplings and R-parity violating couplings all take their natural values which are about (10^0-10^{-2}). Under the family symmetry, only the third generation charged fermions get their masses. This family symmetry is broken in the soft SUSY breaking terms which result in a hierarchical pattern of the fermion masses. It turns out that for the charged leptons, the tau mass is from the Higgs vacuum expectation value (VEV) and the sneutrino VEVs, the muon mass is due to the sneutrino VEVs, and the electron gains its mass due to both Z_{3L} and SUSY breaking. The large neutrino mixing are produced with neutralinos playing the partial role of right-handed neutrinos. |V_{e3}| which is for nu_e-nu_{tau} mixing is expected to be about 0.1. For the quarks, the third generation masses are from the Higgs VEVs, the second generation masses are from quantum corrections, and the down quark mass due to the sneutrino VEVs. It explains m_c/m_s, m_s/m_e, m_d > m_u and so on. Other aspects of the model are discussed.Comment: 25 pages, 3 figures, revtex4; neutrino oscillation and many discussions added, smallness of the electron mass due to supersymmetry pointed out; v3: numerical errors correcte

Our World as an Expanding Shell

In the model where the Universe is considered as a thin shell expanding in 5-dimensional hyper-space there is a possibility to have just one scale for a particle theory corresponding to the Universe thickness. From a realistic model the relation of this parameter to the Universe size was found.Comment: RevTeX, 4 pages, no figure

Uncertainties of the CJK 5 Flavour LO Parton Distributions in the Real Photon

Radiatively generated, LO quark (u,d,s,c,b) and gluon densities in the real, unpolarized photon, calculated in the CJK model being an improved realization of the CJKL approach, have been recently presented. The results were obtained through a global fit to the experimental F2^gamma data. In this paper we present, obtained for the very first time in the photon case, an estimate of the uncertainties of the CJK parton distributions due to the experimental errors. The analysis is based on the Hessian method which was recently applied in the proton parton structure analysis. Sets of test parametrizations are given for the CJK model. They allow for calculation of its best fit parton distributions along with F2^gamma and for computation of uncertainties of any physical value depending on the real photon parton densities. We test the applicability of the approach by comparing uncertainties of example cross-sections calculated in the Hessian and Lagrange methods. Moreover, we present a detailed analysis of the chi^2 of the CJK fit and its relation to the data. We show that large chi^2/DOF of the fit is due to only a few of the experimental measurements. By excluding them chi^2/DOF approx 1 can be obtained.Comment: 28 pages, 8 eps figures, 2 Latex figures; FORTRAN programs available at http://www.fuw.edu.pl/~pjank/param.html; table 10, figure 10 and section 6 correcte

On the H\'enon-Lane-Emden conjecture

We consider Liouville-type theorems for the following H\'{e}non-Lane-Emden system \hfill -\Delta u&=& |x|^{a}v^p \text{in} \mathbb{R}^N, \hfill -\Delta v&=& |x|^{b}u^q \text{in} \mathbb{R}^N, when $pq>1$, $p,q,a,b\ge0$. The main conjecture states that there is no non-trivial non-negative solution whenever $(p,q)$ is under the critical Sobolev hyperbola, i.e. $\frac{N+a}{p+1}+\frac{N+b}{q+1}>{N-2}$. We show that this is indeed the case in dimension N=3 provided the solution is also assumed to be bounded, extending a result established recently by Phan-Souplet in the scalar case. Assuming stability of the solutions, we could then prove Liouville-type theorems in higher dimensions. For the scalar cases, albeit of second order ($a=b$ and $p=q$) or of fourth order ($a\ge 0=b$ and $p>1=q$), we show that for all dimensions $N\ge 3$ in the first case (resp., $N\ge 5$ in the second case), there is no positive solution with a finite Morse index, whenever $p$ is below the corresponding critical exponent, i.e $1<p<\frac{N+2+2a}{N-2}$ (resp., $1<p<\frac{N+4+2a}{N-4}$). Finally, we show that non-negative stable solutions of the full H\'{e}non-Lane-Emden system are trivial provided \label{sysdim00} N<2+2(\frac{p(b+2)+a+2}{pq-1}) (\sqrt{\frac{pq(q+1)}{p+1}}+ \sqrt{\frac{pq(q+1)}{p+1}-\sqrt\frac{pq(q+1)}{p+1}}).Comment: Theorem 4 has been added in the new version. 23 pages, Comments are welcome. Updated version - if any - can be downloaded at http://www.birs.ca/~nassif/ or http://www.math.ubc.ca/~fazly/research.htm